Question

You need to answer each of the following questions. You need to show your work. Your answer should be submitted in an attachment that is in Microsoft or PDF format.
1. Suppose a zero coupon security has a face value of $1000 and a maturity of 5 years. If the return on comparable securities is 6%, calculate the market price of this security.
2. Suppose a coupon security has a face value of $1000, a maturity of 4 years, a coupon rate of 4% and and a yield to maturity of 3% (return on comparable securities). Assuming that the interest payments are made semi-annually, calculate the following:
2A. The value of the coupon payment.
2B. The number of payments received by holders of this security and the value of each payment.
2C. Based on your answer to 2B, calculate the present value of each of one of the payment received by holders of this security.
2D. Based on your answer to 2C, calculate the market price of the security.

Answer 1

1: By formula method

price of the bond = Coupon*(1-1/(1+r)^n)/r + FV/(1+r)^n

= 0+ 1000/(1+6%)^5

= 1000/1.06^5

= $ 747.26

2:

A) Coupon payment=Coupon rate* Face value/2

= 4%*1000/2

= $20

B) Number of payments= 4 years *2 = 8 payments

Value of each payment from 1 to 7= $20

Value of payment no 8= 1000+20 = $1020

C) Preent value= Future value/(1+r)^n where r= 3%/2= 1.5%

Present value of payment 1= 20/(1+1.5%)^1 = 19.70443

Present value of payment 2= 20/(1+1.5%)^2 = 19.41323

Present value of payment 3= 20/(1+1.5%)^3= 19.12634

Present value of payment 4= 20/(1+1.5%)^4= 18.84368

Present value of payment 5= 20/(1+1.5%)^5= 18.56521

Present value of payment 6= 20/(1+1.5%)^6= 18.29084

Present value of payment 7= 20/(1+1.5%)^7 = 18.02054

Present value of payment 8= 1020/(1+1.5%)^8= 905.4653

D) Market price= Sum of the above present values = $1037.43